The generator matrix
1 0 0 0 0 1 1 1 X 1 1 1 1 X X X X 1 X 1 1 0 1 1 0 1 1 1 1 1 X 1 1 1
0 1 0 0 0 0 0 0 1 1 X+1 X+1 X+1 1 X 1 1 X+1 X X 1 0 X 1 1 0 1 0 0 X X X+1 X+1 0
0 0 1 0 0 0 1 1 1 1 X X+1 X X 1 0 X+1 1 1 X+1 X 1 1 X X X+1 0 X 1 X 1 0 1 0
0 0 0 1 0 1 1 0 1 0 X+1 1 X 1 X+1 0 0 X X+1 0 X+1 0 X X+1 X+1 X X+1 X+1 1 X 1 0 1 0
0 0 0 0 1 1 0 1 1 X X+1 X 0 0 0 X+1 X X+1 1 X X+1 1 X+1 0 X+1 X X X 0 1 1 1 X 0
0 0 0 0 0 X 0 0 0 0 0 0 0 X X X X 0 X X 0 X X 0 0 X X X X 0 X 0 0 0
0 0 0 0 0 0 X 0 0 X X 0 0 0 X 0 X X X 0 X 0 X 0 X X 0 X 0 0 0 X 0 0
0 0 0 0 0 0 0 X 0 0 0 X X X 0 X 0 X X X X 0 0 0 0 X X 0 0 X 0 X 0 0
generates a code of length 34 over Z2[X]/(X^2) who´s minimum homogenous weight is 24.
Homogenous weight enumerator: w(x)=1x^0+34x^24+78x^25+175x^26+286x^27+313x^28+410x^29+486x^30+564x^31+637x^32+712x^33+730x^34+686x^35+734x^36+622x^37+528x^38+434x^39+278x^40+192x^41+111x^42+76x^43+49x^44+32x^45+18x^46+2x^47+2x^48+2x^49
The gray image is a linear code over GF(2) with n=68, k=13 and d=24.
This code was found by Heurico 1.16 in 3.43 seconds.